A0180
Title: Density functions from the exponential family as units of Bayes space: A simulation study
Authors: Renata Talska - Palacky University Olomouc (Czech Republic) [presenting]
Karel Hron - Palacky University (Czech Republic)
Alessandra Menafoglio - Politecnico di Milano (Italy)
Abstract: Probability density functions (PDFs) form a special class of functional data, carrying primarily relative information and characterized by specific features like scale invariance and relative scale. The Bayes spaces have been recently developed to capture the relative nature of PDFs by embedding the statistical analysis into an appropriate separable Hilbert space. Density functions from the exponential family form affine subspaces of a Bayes space, whose dimension honours the number of parameters of the distribution. The aim is to analyze possibility of representing and reducing the dimensionality of densities from the exponential family using the Bayes space methodology. For instance, we will show that proper choice of parameters is needed to single out the correct dimensionality of the considered family. Furthermore, functional principal component analysis in the Bayes spaces is employed to reveal interesting features of PDFs from the exponential family. A mapping of PDFs from Bayes spaces to the L2 space (i.e. centred logratio transformation) enables one to work according to the Bayes space geometry, by applying familiar tools of functional data analysis (e.g. FPCA).
